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Appropriate Tightening Axial Force of Bolts / Appropriate Tightening Torque

Tightening axial force and fatigue limit when fastening with bolts
Calculation of tightening axial force and tightening torque
Calculation examples
Initial tightening force and tightening torque

Tightening axial force and fatigue limit when fastening with bolts^*1

Calculation of the appropriate tightening axial force when tightening bolts shall be within the elastic range of 70% of the standard yield resistance at the maximum with the torque method.
Fatigue strength of bolts due to repeated loading shall not exceed the allowable value.
The bolt and nut bearing surfaces are not allowed to cave in due to the fastened object.
Tightening does not damage the fastened object.

Calculation of tightening axial force and tightening torque

The relation of the tightening axial force Ff is shown by equation (1).
Ff＝0.7×σy×As……（1）
Tightening torque Tfa can be obtained from equation (2).
TfA＝0.35k（1＋1/Q）σy・As・d……（2）

k: : Torque coefficient

d: : Bolt nominal diameter [cm]

Q: : Tightening coefficient

σy: : Yield resistance (1098 N/mm² {112 kgf/mm²} when strength class is 12.9)

As: : Bolt effective cross-sectional area [mm²]

Calculation examples

Find the appropriate torque and axial force when tightening mild steel to mild steel with M6 hex socket head cap screw (strength class 12.9) *2 with oil lubrication.

Appropriate torque is calculated from equation (2)
TfA＝0.35k（1＋1/Q）σy・As・d
＝0.35・0.175（1＋1/1.4））1098・20.1・0.6
＝1390［N・cm］{142［kgf・cm］}
Axial force Ff is calculated from equation (1)
Ff＝0.7×σy×As
＝0.7×1098×20.1
＝15449{［N］1576［kgf］}

Torque coefficient due to bolt surface treatment and combination of material of the fastened object and material of the female thread
Bolt surface treatment lubrication	Torque coefficient k	Combination Material of the fastened object (a) - female thread material (b)
Steel bolt black oxide coating oil lubrication	0.145	SCM−FC　FC−FC　SUS−FC
	0.155	S10C−FC　SCM−S10C　SCM−SCM　FC−S10C　FC−SCM
	0.165	SCM−SUS　FC−SUS　AL−FC　SUS−S10C　SUS−SCM　SUS−SUS
	0.175	S10C−S10C　S10C−SCM　S10C−SUS　AL−S10C　AL−SCM
	0.185	SCM−AL　FC−AL　AL−SUS
	0.195	S10C−AL　SUS−AL
	0.215	AL−AL
Steel bolt black oxide coating non- lubrication	0.25	S10C−FC　SCM−FC　FC−FC
	0.35	S10C−SCM　SCM−SCM　FC−S10C　FC−SCM　AL−FC
	0.45	S10C−S10C　SCM−S10C　AL−S10C　AL−SCM
	0.55	SCM−AL　FC−AL　AL−AL

S10C: : Non heat-treated mild steel

SCM: : Heat-treated steel (35JRC)

FC: : Cast iron (FC200)

AL: : Aluminum

SUS: : Stainless steel (SUS304)

Standard value of tightening coefficient Q
Tightening coefficient Q	Tightening method	Surface condition		Lubrication condition
Tightening coefficient Q	Tightening method	Bolt	Nut	Lubrication condition
1.25	Torque wrench	Manganese phosphate	Not treated or phosphate	Oil lubrication or MoS2 paste
1.4	Torque wrench	Not treated or phosphate
1.4	Wrench with torque limit
1.6	Impact wrench
1.8	Torque wrench	Not treated or phosphate	Not treated	No lubrication
1.8	Wrench with torque limit	Not treated or phosphate	Not treated	No lubrication

Strength class expression

Initial tightening force and tightening torque^*2

Nominal thread size	Effective cross-sectional area As mm²	Strength class
		12.9			10.9
		Yield load	Initial tightening force	Tightening torque	Yield load	Initial tightening force	Tightening torque
		N｛kgf｝	N｛kgf｝	N・cm ｛kgf・cm｝	N｛kgf｝	N｛kgf｝	N・cm ｛kgf・cm｝
M3×0.5	5.03	5517{563}	3861{394}	167{17}	4724{482}	3312{338}	147{15}
M4×0.7	8.78	9633{983}	6742{688}	392{40}	8252{842}	5772{589}	333{34}
M5×0.8	14.2	15582{1590}	10907{1113}	794{81}	13348{1362}	9339{953}	676{69}
M6×1	20.1	22060{2251}	15445{1576}	1352{138}	18894{1928}	13220{1349}	1156{118}
M8×1.25	36.6	40170{4099}	28116{2869}	3273{334}	34398{3510}	24079{2457}	2803{286}
M10×1.5	58	63661{6496}	44561{4547}	6497{663}	54508{5562}	38161{3894}	5557{567}
M12×1.75	84.3	92532{9442}	64768{6609}	11368{1160}	79223{8084}	55458{5659}	9702{990}
M14×2	115	126224{12880}	88357{9016}	18032{1840}	108084{11029}	75656{7720}	15484{1580}
M16×2	157	172323{17584}	120628{12309}	28126{2870}	147549{15056}	103282{10539}	24108{2460}
M18×2.5	192	210739{21504}	147519{15053}	38710{3950}	180447{18413}	126312{12889}	33124{3380}
M20×2.5	245	268912{27440}	188238{19208}	54880{5600}	230261{23496}	161181{16447}	46942{4790}
M22×2.5	303	332573{33936}	232799{23755}	74676{7620}	284768{29058}	199332{20340}	63896{6520}
M24×3	353	387453{39536}	271215{27675}	94864{9680}	331759{33853}	232231{23697}	81242{8290}

Nominal thread size	Effective cross-sectional area As mm²	Strength class
		8.8
		Yield load	Initial tightening force	Tightening torque
		N｛kgf｝	N｛kgf｝	N・cm ｛kgf・cm｝
M3×0.5	5.03	3214{328}	2254{230}	98{10}
M4×0.7	8.78	5615{573}	3930{401}	225{23}
M5×0.8	14.2	9085{927}	6360{649}	461{47}
M6×1	20.1	12867{1313}	9006{919}	784{80}
M8×1.25	36.6	23422{2390}	16395{1673}	1911{195}
M10×1.5	58	37113{3787}	25980{2651}	3783{386}
M12×1.75	84.3	53949{5505}	37759{3853}	6605{674}
M14×2	115	73598{7510}	51519{5257}	10486{1070}
M16×2	157	100470{10252}	70325{7176}	16366{1670}
M18×2.5	192	126636{12922}	88641{9045}	23226{2370}
M20×2.5	245	161592{16489}	113112{11542}	32928{3360}
M22×2.5	303	199842{20392}	139885{14274}	44884{4580}
M24×3	353	232819{23757}	162974{16630}	57036{5820}

Notes

^*1 Bolt tightening methods include torque method, torque gradient method, rotation angle method, elongation measurement method, etc., but the torque method is widely used because it is simple.
^*2 Tightening conditions: Use torque wrench (surface oil lubrication, torque coefficient k = 0.17, tightening coefficient Q = 1.4) As torque coefficient changes depending on usage conditions, use this table as a reference.
This table is an edited excerpt from the Kyokuto MFG. Co., Ltd. catalog.